Merge branch 'master' of https://github.com/tforgione/Paella

Code/include/Skeleton/Skeleton.hpp

@@ -14,6 +14,25 @@
 /// \defgroup skeleton Skeleton module
 ///
 /// Module to manage 2D-skeletons
+///
+/// This module contains two programs.
+///   - Skeleton
+///   - SkeletonDrawing
+///
+/// \section Skeleton
+/// This is the main binary. it takes several arguments
+/// \verbatim
+// Allowed options:
+//   -h [ --help ]         produce help message
+//   --img1 arg            first image (for the keypoints detection)
+//   --img2 arg            second image (for the keypoints detection)
+//   --mask1 arg           binary mask of the first image (to remove useless
+//                         keypoints)
+//   --mask2 arg           binary mask of the second image
+//   --skl1 arg            first skeleton, and its branches
+//   --skl2 arg            second skeleton
+//   -o [ --output ] arg   output file
+/// \endverbatim
 ///////////////////////////////////////////////////////////
 
 ///////////////////////////////////////////////////////////

report/subsections/junctions.tex

@@ -45,11 +45,22 @@ X =
  \]
 Then subtract it with the centroid matrix associated.
 \[ 
- X - X_{m}
+ X_{c} = X - X_{m}
 \]
-The normal vector of the best-fitting plane is the left singular vector corresponding to the least singular value of \[ XX^T \]
+The normal vector $N$ of the best-fitting plane will be the cross product of the 2 eigenvectors $v_1,v_2$ corresponding to the two biggest singular values of the covariance matrix of $X_{c}$ : 
+\[
+ X_{c}X_{c}^T
+ \]
+ \[
+ N = v_1 \wedge v_2
+ \]
 
 Then to compute the constant value of the equation we use the centroid.
+\[
+d = -N*X_m
+\]
+
+At the end we have the parameters of the plane in N and d.
 
 \begin{figure}[H]
    \begin{center}